Read the following and answer any four questions from (i) to (v)
Gayathri Wanted to see the stars in the night sky. She is aware that a telescope is required to glimpse such far-off stars. She understood that telescopes made from mirrors are called reflecting telescopes while telescopes made from lenses are called refracting telescopes.
So, she decided to make a refracting telescope. She bought two lenses, L₁which is bigger than L₂. While the smaller lens enlarges the image, the larger lens collects and bends the light. Large, heavy lenses have more power. Therefore, she required a large, powerful lens to look far away. Sadly, she discovered that a large lens is rather hefty. Making heavy lenses and positioning them correctly is challenging. In addition, because they transmit light, lenses must have exceptionally smooth surfaces. False in the lenses would cause the image to become distorted. It would be like looking through a dirty window.
(i) What type of lenses would Gayathri require to construct the telescope based on the given diagram?
a) concave lenses
b) convex lenses
c) Bifocal lenses
d) Flat lenses
(ii) What would be the ratio of the focal length of L₁ and L₂, if the powers of the lenses L₁ and L₂ are in the ratio of 5: 1?
a) 5: 1
b) 1: 5
c) 2: 1
d) 1: 1
(iii) What is the equation for the magnification that a lens produces?
a) Ratio of the height of the image to the height of the object
b) Double the focal length
c) Inverse of the radius of curvature
d) Inverse of the object distance
(iv) Gayathri did some preliminary experiment with the lenses and found out that the magnification of the eyepiece (𝐿₂) is 4. If in her experiment with L₂she found an image at 28 𝑐𝑚 from the lens, at what distance did she put the object?
(a) 72 𝑐𝑚
(b) 12 𝑐𝑚
(c) 8 𝑐𝑚
(d) 7 𝑐m
(v) For the telescope, Gayathri purchased thinner lenses and polished them. What benefits, if any, will her selection of lenses provide?
a) She will not have any advantage as even thicker lenses would give clearer images.
b) thicker lenses would have made the telescope easier to handle.
c) Not-so-thick lenses would not make the telescope very heavy and also allow a considerable amount of light to pass.
d) Not-so-thick lenses will give her more magnification.

Question

Read the following and answer any four questions from (i) to (v)
Gayathri Wanted to see the stars in the night sky. She is aware that a telescope is required to glimpse such far-off stars. She understood that telescopes made from mirrors are called reflecting telescopes while telescopes made from lenses are called refracting telescopes.
So, she decided to make a refracting telescope. She bought two lenses, L₁which is bigger than L₂. While the smaller lens enlarges the image, the larger lens collects and bends the light. Large, heavy lenses have more power. Therefore, she required a large, powerful lens to look far away. Sadly, she discovered that a large lens is rather hefty. Making heavy lenses and positioning them correctly is challenging. In addition, because they transmit light, lenses must have exceptionally smooth surfaces. False in the lenses would cause the image to become distorted. It would be like looking through a dirty window.
(i) What type of lenses would Gayathri require to construct the telescope based on the given diagram?
a) concave lenses
b) convex lenses
c) Bifocal lenses
d) Flat lenses
(ii) What would be the ratio of the focal length of L₁ and L₂, if the powers of the lenses L₁ and L₂ are in the ratio of 5: 1?
a) 5: 1
b) 1: 5
c) 2: 1
d) 1: 1
(iii) What is the equation for the magnification that a lens produces?
a) Ratio of the height of the image to the height of the object
b) Double the focal length
c) Inverse of the radius of curvature
d) Inverse of the object distance
(iv) Gayathri did some preliminary experiment with the lenses and found out that the magnification of the eyepiece (𝐿₂) is 4. If in her experiment with L₂she found an image at 28 𝑐𝑚 from the lens, at what distance did she put the object?
(a) 72 𝑐𝑚
(b) 12 𝑐𝑚
(c) 8 𝑐𝑚
(d) 7 𝑐m
(v) For the telescope, Gayathri purchased thinner lenses and polished them. What benefits, if any, will her selection of lenses provide?
a) She will not have any advantage as even thicker lenses would give clearer images.
b) thicker lenses would have made the telescope easier to handle.
c) Not-so-thick lenses would not make the telescope very heavy and also allow a considerable amount of light to pass.
d) Not-so-thick lenses will give her more magnification.

Infinity Learn · Accepted Answer

(i) Based on the diagram, Gayathri needs convex lenses to make the telescope.

(ii)

$P = \frac{1}{f} \Rightarrow P_{1} = \frac{1}{f_{1}} . . . . . . . (a) \Rightarrow P_{2} = \frac{1}{f_{2}} . . . . . . . . (b) \Rightarrow \frac{P_{1}}{P_{2}} = \frac{5}{1} . . . . . . . . . (c)$

Putting the value of P₁ and P₂ from Equations (a) and (b) in equation (c)

$\Rightarrow \frac{\frac{1}{f_{1}}}{\frac{1}{f_{2}}} = \frac{5}{1} Hence, \frac{f_{1}}{f_{2}} = \frac{1}{5} The ratio of the focal lengths of L_{1} and L_{2} is 1 : 5 . Hence, the correct option is b) 1 : 5$

(iii) Magnification is the process through which spherical lenses increase the size of the image in relation to the object size. It is the ratio of the image height (h₁) to the object height (h₂) is indicated by the symbol (m).

$m = \frac{h_{1}}{h_{2}}$

Hence, the correct option is a) Ratio of the height of the image to the height of the object.

(iv) We know that $m = \frac{v}{u}$

Where m is the magnification

u is the distance of the object from the pole of the mirror

v is the distance of the image from the pole of the mirror

$m = 4; v = 28 cm (Given)$

$Hence, 4 = \frac{28}{u}$

$Thus, u = 7 cm$

Hence, the correct option is d) 7 cm.

(v) Gayathri has the advantage with her choice of lenses is that not-so-thick lenses would not make the telescope very heavy and also allow a considerable amount of light to pass.

Hence, the correct option is c) Not-so-thick lenses would not make the telescope very heavy and also allow a considerable amount of light to pass.

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